This invention relates to the determination of the surface contours of objects and, more particularly, to an improved apparatus and method for determining three dimensional surface profiles of objects, including 360 degree renditions thereof.
Surface profile measurement by non-contact optical methods has been extensively studied because of its importance in fields such as automated manufacturing, component quality control, medicine, robotics, and solid modeling applications. In most of these methods a known periodic pattern, such as a grating, is projected on the surface to be measured and the image of the grating, deformed by the surface, is analyzed to determine the profile. "Demodulation" of the deformed grating by means of a matched reference grating results in the well known Moire fringe patterns, which are easily interpretable as surface contours by a human observer, but, are somewhat more complicated for computer analysis. (See, for example, D. M. Meadows, W. O. Johnson and J. B. Allen, Appl. Opt. 9, 942 (1970); H. Takasaki, Appl. Opt. 9, 1467 (1970); P. Benoit, E. Mathieu, J. Hormiere and A. Thomas, Nouv. Rev. Opt. 6, 67 (1975); T. Yatagai, M. Idesawa and S. Saito, Proc. Soc. Photo-Opt. Instrum. Eng. 361, 81 (1982)). Improvements to the Moire method, aimed at increasing accuracy and at automating the measurements have been based, for example, on phase modulation. (See G. Indebetouw, Appl. Opt. 17, 2930 (1978), D. T. Moore and B. E. Truax, Appl. Opt. 18, 91 (1979).
An alternative approach to Moire is by an analysis of the deformed grating itself without the use of a physical or virtual reference grating. Direct methods based on geometrical analysis of the deformed grating requiring fringe peak determination are computationally complex, slow, and result in low accuracy. Another direct method, based on the use of a Fast Fourier Transform analysis of the deformed grating, has been demonstrated to be more suitable for automated profilometry (see, for example, M. Takeda and K. Mutoh, Appl. Opt. 22, 3977 (1983)). Limitations on measurement of steep object slopes and step discontinuities, the need for high resolution imaging systems and the need for powerful computing capability are some of the disadvantages of the Fast Fourier Transform method.
An approach to obtaining a complete 360 degree view of a general three-dimensional object, which has been the subject of intense activity, especially in computer vision research, is the reconstruction of three-dimensional shapes from several objects views, as seen from different points of observation. It generally involves the use of elaborate computer algorithms to `match` these views in order to unify the images to determine the complete object shape. [See, for example, B. Bhanu, "Representation and Shape Matching of 3-D Objects", IEEE Trans. Anal. Machine Intell. PAMI-6, 340 (1984).] Such a digital image processing approach is computation intensive and generally offers limited accuracy.
Another approach involves the use of the shadow moire method in conjunction with a periphery camera. It tends to be mechanically cumbersome and to require tedious processing of fringe patterns recorded on film. [See, for example, C. G. Saunders, "Replication from 360-degree Moire Sensing", in `Moire Topography and Spinal Deformity`, M. S. Moreland, et al., EDS., Pergamon Press, New York, (1981), p. 76.]
In the parent application hereof, and as described in an article entitled "Automated Phase-Measuring Profilimetry of 3-D Diffuse Objects" by V. Srinivasan, H. C. Liu, and M. Halioua, Applied Optics, Vol. 23, No. 18, Sept. 15, 1984, there is disclosed a technique which employed, inter alia, phase measuring techniques that were used in classical interferometry, but were found to be particularly advantageous for use in deformed grating profilometry. When a sinusoidal intensity distribution is projected on a three dimensional diffuse surface, the mathematical representation of the deformed grating image intensity distribution is similar to that encountered in conventional optical interferometry. The surface height distribution can be translated to a phase distribution, and the accuracy which is characteristic of phase modulation interferometry, was used to advantage. [See, for example, J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White and D. J. Brangaccio, Appl. Opt. 13, 2696 (1974); J. C. Wyant, Appl. Opt. 14, 2622 (1975) for background.] It was noted that by using several phase modulated frames of deformed grating image data, a high degree of precision in the phase measurement can be achieved. By analogy with phase-measuring interferometry, where phase values can be measured with a resolution of 1/1000 of a fringe period (versus 1/30 for conventional single frame interferometry), surface profile measurements with less than 10 micron resolution were noted to be possible by the use of an optical system with a projected grating pitch in the millimeter range.
In accordance with an embodiment of the method in the parent application hereof and in the referenced Srinivasan, Liu and Halioua article, a technique was set forth for determining the surface profile of a three-dimensional object. In the method, an incident beam of light, having a sinusoidally varying intensity pattern, is directed at the object. The phase of the sinusoidal pattern of the incident beam is modulated. A deformed grating image of the object is received, at a detector array, for a number of different modulated phases of the input beam. The height of each point (i.e., elemental region) of the surface of the object is then determined with respect to a reference plane, each such height determination including the combining of the image intensity values at a detector position corresponding to a respective point of the object.
Among the advantages of the technique are the following: relatively simple optical hardware; relatively low frequency grating and low density detector array; full frame data capture and relatively simple processing.
It is an object of the present invention to provide further improvement, and a technique which is applicable to efficient and automatic obtainment of a three dimensional surface profile of an object, including the capability of obtaining a complete 360 degree surface profile.